20

CO

ONCERNING the Principles of the Do&trine of

the Sphere, and Spherical Projection and Trigono-

melry, in fifty four Definitions

Page 1

Chap. II.

Containeth twelve Theorems serving to the Orthographic

Proje{lion of the Spheré, called the Analemma, in

Plano

Chap. III.

Containeth Problems of the Orthographic Projection, viz.

19

Prob. 1. To describe an Ellipsis

19

Prob. 2. To divide a Right Circle into its proper Degrees

Prob. 3. To divide an Oblique Circle into its proper De-

grees

Prob. 4. To projeầt the Sphere on the Solftitial Colure 22

Prob. 5. To describe the Hour Circles, Azimuths, &c. 24

Prob. 6. To divide the Ecliptic into the twelve Signs of

the Zodiac

25

Prob. 7. To annex the Calendar to the Analemma ibid.

Prob. 8. To shew the Uses of this Proje£tion in general 26

Prob. 9. To exhibit a Synopsis of the Astronomical Affecti-

ons of the Heavens for any given Time thereby 28

Prob. 10. To represent the fixed Stars on this ProjęEtion

29

Chap,

21

ibid.

Chap. IV.

Contaireth eleven Theorems ferving to the Stereographic

Projection of the Sphere in Plano

30

Chap. V.

Containeth Problems of the Stereographic Projetion, viz.

42

Prob. 1. To find the Pele of any Great Circle

Prob. 2. To describe, or lay down, any Spherical Angle

43

Prob. 3. To draw a Great Circle through any given

Point, so as to contain any given Angle with the Pri-

mitive

44

Prob. 4. To describe a Great Circle through any two

Points given within the Primitive

45

Prob. 5. To measure any Spherical Angle

46

Prob. 6. To divide any Great Circle into its proper De-

grees

48

Prob. 7. To draw any parallel Circle

49

Prob. 6. To draw a Great Circle perpendicular to any

other

51

Prob. 9. To graduate any lesser Oblique Circle 52

Chap. VI.

The Stereographic Projection of the Sphere on the Planes

of several Great Circles of the Spbere.

53

Viz. i. On the Plane of the General Meridian 55

2. On the Plane of the Horizon of London 56

3. On the Plane of the Ecliptic

62

4. On the Plane of the EquinoEtial

5. On the Plane of the Tropic of Capricorn 68

6. On the Plane of any Oblique Circle 70

Chap. VII.

Containeth Forty One Theorems for the Explication of the

Doctrine of Spherical Triangles in general ; by which

is sewn the Reason of the several Canons for their

Solution

74

65

/

Chap.

II2

124

Chap. VIII.

Of the Nature, Cases, Analogies, and various Methods

of Solving Right-angled Spherical Triangles ; with a

Synopsis of the Whole Do&trine

98

Chap. IX.

Method 1. Of solving Right-angled Spherical Triangles

by the Logarithmetic Canon of Sines and Tangents

105

Chap. x.

Method 2. By Natural Sines and Tangents

Chap. XI.

Method 3. By the Lord Neiper's Five Circular Parts

117

Chap. XT.

Method 4. By the Sesicr

Chap. XIII.

Method 5. By the Sliding-Rule

131

Chap. XIV.

Method 6. By Gunter's Scale, and Compasses

138

Chap. XV.

Method 7. By the Artificial Globe, or Sphere 143

Chap. XVI.
Method 8. By the Stereographic Projetion

150

Chạp. XVII.

Method 9 and 10. By the Orthographic and Stereogra-

phic Planispheres

161

Chap. XVIII.

Of the Doctrine of Oblique-angled Spherical Triangles ;

a Synopsis of the fix Cafes thereof ; the Method of
Solving them by letting fall a Perpendicular ; aid
Rules for solving all kind of Ambiguities attending

them

166

Chap. XIX.

Method of solving Oblique Spherical Triangles without a

Perpendicular ; with a proper Scheme for the Demon

ftration thereof

118

Chap.

a 2

200

Chap. XX.

The Solution of the six Cafes of Oblique Triangles by Ste-

reographic Projeétion

Chap. XXI.

Tha Mensuration of the Area of a Spherical Triangle ;

and the Completion of a solid Body ; with Examples

208

of each

PART II.

CH A P. I.

213

221

Containing the Application of Spherical Trigonometry

to Astronomy ; in all the praEtical Problems of the

Sun, Moon, and Stars ; with Tables of the Sun's Mo-

tion, for Years, Montbs, Days, Hours, Minutes, and

Seconds. The Problems are as follow

Viz. Prob. 1. To find the Sun's Place at any time by

tbe Tables

Prob. 2. To find the Latitude of any Place

224

Prob 3. To find the Sun's Greatest Declination 225

Prob. 4. To find the Sun's Present Declination 226

Prob. 5. To find the Sun's Right Ascension 227

Prob. 6. To find the Sun's Place, and Right Ascen-
fron otherwise

ibid.

Prob. 7. To find the Angle of the Sun's Position 228

Prob. 8. To find the Sun's Amplitude of Rising

and Setting

ibid.

Prob.

9. To find the Ascensional Difference ; or the

true Time of the Sun's Rising and Setting 230

Prob. 10. To find the Sun's Oblique Ascension and

Descension

231

Prob. 11. To find the Time the Sun is due East or

Weft

232

Prob. 12. To find bis Altitude when due East or

West

233

Prob.

Prob. 13. To find the Sun's Azimuth at the Hour

of fix

234

Prob. 14. To find his Altitude at the Hour of fix

235

Prob. 15. To find the Sun's Altitude at any time

of Day

236

Prob. 16. To find the Hour of the Day 240

Prob. 17. To find the Sun's Azimuth at any time

241

Prob, 18. To find the Sun's Apparent Rising, Set-

ting, and Amplitude

243

Prob. 19. To find the Beginning and End of Twi-

light

246

Prob. 20. To find the Declination of a Star or

Planet

248

Prob. 21. To find its Right Ascension 251

Prob. 22. To find its Longitude and Latilude 252

Prob. 23. To find the Hour of the Night 254

Prob. 24. To find the Culminating Point in ibe

Ecliptic

256

Prob. 25. To find the Meridian Angle 257

Prob. 26. To find the Declination of the Culmina-
ting Point

ibid.

Prob. 27. To find the Altitude thereof 258

Prob. 28. To find the Altitude of the Nonagesima

ibid.

Prob. 29. To find the Place thereof in the Ecliptic

259

Prob. 30. To find the Cufp of the Ascendant, or

Horoscope

260

Prob. 31. To find the Parallactic Angle ibid.
Prob. 32. To find the Cosmical Rising of a Star,
&c.

261

Prob. 33. To find the Time of its Cosmical Setting

263

Prob. 34. To find the time of its Achronical Rising

and Setting

264

Prob.

Degree